On the Deficiency of Bipartite Graphs

Given a graph G, an edge-coloring or G with colors 1,2.3.. is consecutive if the colors of edges incident to each vertex fomm an interval of integer-s. This papelis devoted to bipartite graphs which do not have such a coloring of edges. We investigate their consecutive coloring deficiency, or shortly the deficiency d(G) of G, i.e. the minimum number of pendant edges whose attachment to G makes it consecutively colorable. In particular. we show that there are bipartite graphs whose deficiency approaches the number of vertices.